The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

Anthropological approaches to studying the contextual specificity of mathematical thought and practice in schools can productively inform descriptions and analyses of mathematical practices within and across different teaching and learning contexts. In this paper I argue for an anthropological methodological orientation that takes into…

In the present study we examined whether children with Developmental Dyscalculia (DD) exhibit a deficit in the so-called "Approximate Number System" (ANS). To do so, we examined a group of elementary school children who demonstrated persistent low math achievement over 4 years and compared them to typically developing (TD), aged-matched…

Comparing numerical performance between different languages does not only mean comparing different number-word systems, but also implies a comparison of differences regarding culture or educational systems. The Czech language provides the remarkable opportunity to disentangle this confound as there exist two different number-word systems within…

Recently, the nature of children's mental number line has received much investigation. In the number line task, children are required to mark a presented number on a physical number line with fixed endpoints. Typically, it was observed that the estimations of younger/inexperienced children were accounted for best by a logarithmic function, whereas…

Ordinality is--beyond numerical magnitude (i.e., quantity)--an important characteristic of the number system. There is converging empirical evidence that (intra)parietal brain regions mediate number magnitude processing. Furthermore, recent findings suggest that the human intraparietal sulcus (IPS) supports magnitude and ordinality in a…

Adults can represent approximate numbers of items independently of language. This approximate number system can discriminate and compare entities as varied as dots, sounds, or actions. But can multiple different types of entities be enumerated in parallel and stored as independent numerosities? Subjects who were prevented from verbally counting…

This study examined the neuronal correlates of reading Roman numerals and the changes that occur with extensive practice. Subjects were scanned by functional Magnetic Resonance Imaging (fMRI) three times the first day of the experiment and once following two to three months of practice. This allowed comparison of brain activations with varying…

Analyzed construction of approximative expressions with two numerals in Dutch. Found that choice of number words was not arbitrary and that various kinds of factors are involved. Results suggest that analogue magnitude code is used in estimating and comparing, and human cognition seems to be able to perform simple calculations with quantities,…

Some pedagogical problems in Chinese numeration are described. They involve the teaching and learning of how to speak numerals with fluency in Chinese, using Hindu-Arabic written numbers. An alternative approach which stresses regularity is proposed. (MNS)

In this study, Piagetian theory is extended to explore ways in which children construct their understanding of our notational system and place value. Eighty children aged 4 to 9 were asked to group objects, draw pictures of grouped quantities, write numerals to indicate amounts, and theorize about the relationship between their written numerals…

A mathematics teacher who avoided students' questions about zero, notes that children are able to interpret this concept and any system of numeration in a language that they have made up and can understand. (AM)

The NCTM curriculum states that students should be able to "compare and contrast the real number system and its various subsystems with regard to their structural characteristics." In evaluating overall conformity to the 1989 standard, the National Council of Teachers of Mathematics (NCTM) requires that "teachers must value and encourage the use…

Children's reported use of single and multiple search strategies during a matching numbers task, along with accompanying verbal (private speech, self-talk) and motoric (finger pointing, place-holding) strategic behaviors were examined with a large, nationally representative cross-sectional sample ("n"=1,979) of children between the ages of 5 and…

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)